Worksheet on H.C.F. of Monomials

Practice the worksheet on H.C.F. of monomials. The questions are based on finding the highest common factor of two or more monomials. 

We know, the highest common factor (H.C.F.) of two or more monomials is the monomial of highest dimensions which divides each of them without remainder.

For example: The highest common factor of m⁶, m⁵, m⁴, m³, m² is m².

If the monomials have numerical coefficients, find by Arithmetic their greatest common measure, and prefix it as a coefficient to the algebraical highest common factor.

For example: The highest common factor of 14m⁴a³b, 21m²a⁴b and 35m³ab⁴ is 7m²ab; for it consists of the product of:

(i) the greatest common measure of the numerical coefficients;

(ii) the highest power of each letter which divides everyone of the given expressions.

1. Find the highest common factor (H.C.F.) of the two monomials:

(i) a²b and a²b²

(ii) a²b²c³ and a²b²c²

(iii) 15x²y³ and 6x³y²

(iv) 4a² and 10ab

(v) 21x²y and 49xy²

(vi) a³b² and – 5b²

(vii) 26a³y²k⁴ and 39a²y⁴k²

(viii)24m²n³ and 32m³n⁴

(ix) 81x²y⁴z² and 18x³y³z

(x) 18x³y²z⁴ and 54x²y⁴z

(xi) 20a²b³c⁴ and 70a³b²z²

(xii) 16x²y³ and 60x³y²

2. Find the highest common factor (H.C.F.) of the three monomials:

(i) 3x²y², 6x³y and 4x⁴y²

(ii) 13x²y³, 17x²y²m and 7m²z

(iii) 8a²m, 6abmn and 10abm³n²

(iv) 49ma², 63mb² and 56mc²

(v) 17xy²z, 34x²yz and 51xyz²

(vi) 25ab²c, 100a²bc and 125ab

(vii) 4a³, 6b² and 8c

(viii) 2m²n³, 10m³n², 14mn

(ix) 5z³, - 15z² and 45z

(x) 42p²q²r, 63p³q and 56p²r

(xi) 15x⁵y³z⁷, 60x³y⁷z⁶ and 25x⁴y⁵z²

(xii) 35p²qr³, 42p³q²r and 30pq²r³

Answers for the worksheet on H.C.F. of monomials are given below to check the exact answers of the above questions.

Answers:

1. (i) a²b

(ii) a²b²c²

(iii) 3x²y²

(iv) 2a

(v) 7xy

(vi) b²

(vii) 13a²y²k²

(viii) 8m²n³

(ix) 9x²y³z

(x) 18x²y²z

(xi) 10a²b²z²

(xii) 4x²y²



2. (i) x²y

(ii) 1

(iii) 2am

(iv) 7m

(v) 17xyz

(vi) 25ab

(vii) 2  

(viii) 2mn 

(ix) 5z

(x) 7p²

(xi) 5x³y³z²

(xii) pqr

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